Augmenting Density Matrix Renormalization Group with Matchgates and Clifford circuits

TL;DR

This paper introduces MCA-MPS, a novel wave-function ansatz combining matchgates and Clifford circuits with matrix product states, enhancing classical simulation of quantum many-body systems.

Contribution

It proposes a new MCA-MPS ansatz that leverages matchgates and Clifford circuits within the DMRG framework for improved accuracy in quantum simulations.

Findings

MCA-MPS significantly improves ground-state energy accuracy.

Benchmark results show orders of magnitude improvement over standard MPS.

The method expands understanding of classically simulatable quantum states.

Abstract

Matchgates and Clifford circuits are two types of quantum circuits which can be efficiently simulated classically, though the underlying reasons are quite different. Matchgates are essentially the single particle basis transformations in the Majorana fermion representation which can be easily handled classically, while the Clifford circuits can be efficiently simulated using the tableau method according to the Gottesman-Knill theorem. In this work, we propose a new wave-function ansatz in which matrix product states are augmented with the combination of Matchgates and Clifford circuits (dubbed MCA-MPS) to take advantage of the representing power of all of them. Moreover, the optimization of MCA-MPS can be efficiently implemented within the Density Matrix Renormalization Group method. Our benchmark results on one-dimensional hydrogen chain show that MCA-MPS can improve the accuracy of the ground-state calculation by several orders of magnitude over MPS with the same bond dimension. This new method provides us a useful approach to study quantum many-body systems. The MCA-MPS ansatz also expands our understanding of classically simulatable quantum many-body states.